Rescued a very nice Pioneer SX-650 this weekend. Was curious if anyone had suggestions about specific speakers that would match well with it. I have a set of Sony bookshelf speakers, and while they sound fine, they just won't allow me to turn up the volume past about 1/3 of the way without distorting.

I can think of 2 reasons for this. 1) There is a problem with the receiver, resulting in the distortion you observe. 2) The receiver is OK, but the speakers require more power than the receiver can supply, for the loudness level you desire. The position of the volume control is not an important indicator.

The pioneer has an output rated at 35 watts into 8 ohms. What are the Sony speaker ratings? It sounds unlikely given modest amp power but it could be that the speakers are clipping. or maybe the pioneers capacitors are failing. Regardless it's worth checking out the Sony specs to see if there's a match on paper

Klipsch made some good speakers which would mate well with that Pioneer SX650. All of the Sony speakers that I ever owned were cheaply made and never sounded very good . Some of the HPM series speakers that Pioneer made sounded good and should match well with the SX650. I had the HPM100's and liked them. The distortion you mentioned could be from the stereo or the speakers. Suggestions: with power off, gently push the Sony's woofers in and out by hand to feel if the voice coil form
is rubbing anything or hitting the magnet in back. You should be able to flex that woofer in/out without rubbing against anything or touching the magnet. If it rubs as you move it, or hits the back magnet, it's damaged. On the Pioneer receiver check to hear if there's any static as you rotate the volume control, or any scratch/static from some of the push switches or other rotary contols. If so, try cleaning the controls with electronic contact cleaner. Generally speaking, you should be able to hear good clear audio with the volume control up to or less than the 12 o'clock position depending on source level.( try a cd player or vinyl turntable.) The correct match between speakers and receiver is an opinion, but look for more efficient speakers for your SX650. Room acoustics , speaker efficency and receiver power all contribute (in that order) to the overall musical sound level. If you can achieve the volume you like, in your specific room, with one pair of speakers and the volume control
on the Pioneer less than 12 o'clock that would be a good match. Don't run more than 1 pair of speakers at a time.
Per your request , speaker suggestions : Klipsch Heresy's, JBL L100's, Dahlquist DQM9's, Pioneer HPM 100's, and
some of the Yamaha pro monitors were ok too (I forget the #'s on the one's I had-good heavy cabinets 3-way with white woofers)
Floor standing speakers are usually more efficient than bookshelf speakers within the same speaker line. Try to get speakers which produce the loudness you want with the Pioneer volume control set between 9 o'clock to 11 o'clock
position. This leaves reserve capacity for the peaks of the music which are the real volume control. Klipsch LaScalla's would rock with that SX650. My guess is that the Sony " bookshelf" speakers will be limiting your volume level if the Pioneer SX650 is working correctly with clean controls. good luck.